Draw a Diagram and Solve a Simpler Problem

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What You'll Learn

And Why

Solving a Problem Using Two Different Methods

When to Use These StrategiesYou can draw a diagram to show a problem visually. For problems that seem to have an overwhelming number of steps, you can solve a simpler problem that is similar. These strategies are used as alternative methods in Example 1.

Using Strategies

A worm is trying to escape from a well 10 ft deep. The worm climbs 2 ft per day, but each night it slides back 1 ft. How many days will the worm take to climb out of the well?

The total distance to travel is 10 ft. The worm gains 2 ft during the day, but loses 1 ft each night. The goal is to find out how many days the worm will take to get out of the well.

The worm will take 2 days to climb out of a 3-ft well and 3 days to climb out of a 4-ft well. So it would take 9 days to climb out of a 10-ft well.

Your first thought might have been that the worm progresses 1 ft each day and therefore needs 10 days to escape. The worm does move a total of 1 ft each day, except on the ninth day. On the ninth day it climbs 2 ft and reaches the edge of the well.